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# Because all that is being done is to reclassify the

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Unformatted text preview: Because all that is being done is to reclassify the outcomes into success and failures Y will also be binomial. (Ignore the unlikely complication of the index staying the same.) ( ) = (1 − ) = 1.75 ( ) = (5 − ) = 5 − 3.25 = 1.75 and ( ) = (1 − ) = 1.1375 ( ) = (5 − ) = ( − ) = ( − 1) 2 ( ) = ( ) So . . ( ) = [ ( )] 1 ¡ = √ 1.1375 = 1.067 . 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 1 2 3 4 5 Probability Number of increases Stock index increases over 5 years 4. In each of the following cases X is a count. Does it have a binomial distribution? Justify you answer in each case. (a) You observe the sex of the next 20 babies born at a local hospital; X is the number of girls among them. Yes • Recall our concerns about the gender composition example used in lectures: the fertility decision about whether to have a third child or not being impacted by the gender mix of the first two children; possibility of multiple births. These are not relevant here. • Independence across trials now refers to births to different women and having a girl is not contagious! (b) A couple decides to continue to have children until their first girl is born; X is the total number of children the couple has. No • Here n is not fixed and depends on previous trial outcomes. 5. The amount of petrol sold daily by a service station is known to be uniformly distributed between 4,000 and 6,000 litres. What is the probability of sales on any one day being between 5,500 and 6,000 litres? ( ) = 1 2000 4000 ≤ ≤ 6000 = 0 ℎ ∴ (5500 ≤ ≤ 6000) = 500/2000 = 0.25 6. A software random number generator is designed to produce numbers within a specified range. We can consider any number in the range as a possible outcome. Suppose the random number Y can be any value between 0 and 2. Then the uniform density of the outcomes of Y will have a constant height between 0 and 2 and be zero elsewhere. height between 0 and 2 and be zero elsewhere....
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